{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3m0UJN9_lZBK",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "# Taylor-Green Vortex\n",
    "\n",
    "[![Google Collab Book](https://colab.research.google.com/assets/colab-badge.svg)](https://colab.research.google.com/github/tum-pbs/PhiFlow/blob/develop/examples/grids/Taylor_Green.ipynb)\n",
    "\n",
    "The Taylor-Green vortex is a special solution to the Navier-Stokes equations whose shape does not change over time. It only decays exponentially."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "id": "-NuGPniRlX3u",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "%pip install phiflow\n",
    "from phi.jax.flow import *\n",
    "# from phi.flow import *  # If JAX is not installed. You can use phi.torch or phi.tf as well.\n",
    "from tqdm.notebook import trange\n",
    "from functools import partial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vortex decays exponentially, resulting in small numbers at later times. Therefore, we set the global precision to FP64 (double), which affects all future operations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "math.set_global_precision(64)  # double precision for all following operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's define our simulation settings.\n",
    "We use a relatively low viscosity of 0.1, corresponding to a Reynolds number of 1/vis = 10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "domain = dict(x=25, y=25, boundary=PERIODIC, bounds=Box(x=2*PI, y=2*PI))\n",
    "viscosity = 0.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4NTkTx18nitZ",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "## Closed-Form Solution\n",
    "\n",
    "The Taylor–Green vortex is an unsteady incompressible flow of a decaying vortex, and has an analytic solution, given below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "id": "0FBmhDCAsx-T",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "def taylor_green_velocity(x, t):\n",
    "    sin_x, sin_y = math.sin(x).vector\n",
    "    cos_x, cos_y = math.cos(x).vector\n",
    "    return vec(x=cos_x*sin_y, y=-sin_x*cos_y) * math.exp(-2 * viscosity * t)\n",
    "\n",
    "def taylor_green_pressure(x, t):\n",
    "    return -1 / 4 * (math.sum(math.cos(2 * x), 'vector')) * math.exp(-4 * viscosity * t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "STWLmyfb12eh",
    "pycharm": {
     "name": "#%% md\n"
    }
   },
   "source": [
    "We sample the velocity on a [staggered grid](https://tum-pbs.github.io/PhiFlow/Staggered_Grids.html) and the pressure at the cell centers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 1000
    },
    "id": "gUg4_lxJvyJj",
    "outputId": "e10326c5-037f-4776-8cde-12e88a306c8a",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "\n",
    "time = math.linspace(0, 10., batch(time=200))\n",
    "analytic_v = StaggeredGrid(partial(taylor_green_velocity, t=time), **domain)\n",
    "analytic_p = CenteredGrid(partial(taylor_green_pressure, t=time), **domain)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "\">\n",
       "  Your browser does not support the video tag.\n",
       "</video>"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x1de3e5afb80>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot({\"Velocity\": analytic_v.time[::4], \"Pressure\": analytic_p.time[::4]}, animate='time', same_scale=False)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulation\n",
    "\n",
    "Let's simulate the vortex with the same settings and initial conditions we used above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "1HnN9_KZuBpq",
    "pycharm": {
     "name": "#%%\n"
    }
   },
   "outputs": [],
   "source": [
    "@jit_compile\n",
    "def step(velocity, pressure, dt):\n",
    "  velocity = diffuse.explicit(velocity, viscosity, dt)\n",
    "  velocity = advect.semi_lagrangian(velocity, velocity, dt)\n",
    "  return fluid.make_incompressible(velocity, (), Solve('CG', 1e-12, 1e-12, x0=pressure))\n",
    "\n",
    "dt = time.time[1] - time.time[0]\n",
    "v0, p0 = analytic_v.time[0], analytic_p.time[0]\n",
    "sim_v, sim_p = iterate(step, time.shape-1, v0, p0, dt=dt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can plot the simulation error over time."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 864x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rmse = math.sqrt(math.mean((analytic_v - sim_v).values**2))\n",
    "relative_err = rmse / math.mean(abs(analytic_v.values))\n",
    "plot({\"RMSE\": rmse.time.as_spatial(), \"Relative Error\": relative_err.time.as_spatial()})"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
